20 October 2006 A model to predict the critical velocity for liquid loss from a receding meniscus
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This paper is a revision of the authors' previous work entitled "Experimental characterization of the receding meniscus under conditions associated with immersion lithography," presented in Optical Microlithography XIX, edited by Donis G. Flagello, Proceedings of SPIE Vol. 6154 (SPIE, Bellingham, WA, 2006) 61540R. Several engineering challenges accompany the insertion of the immersion fluid in a production tool, one of the most important being the confinement of a relatively small amount of liquid to the under-lens region. The semiconductor industry demands high throughput, leading to relatively large wafer scan velocities and accelerations. These result in large viscous and inertial forces on the three-phase contact line between the liquid, air, and substrate. If the fluid dynamic forces exceed the resisting surface tension force then residual liquid is deposited onto the substrate that has passed beneath the lens. Liquid deposition is undesirable; as the droplets evaporate they will deposit impurities on the substrate. In an immersion lithography tool, these impurities may be transmitted to the printed pattern as defects. A substantial effort was undertaken relative to the experimental investigation of the static and dynamic contact angle under conditions that are consistent with immersion lithography. A semi-empirical model is described here in order to predict the velocity at which liquid loss occurs. This model is based on fluid physics and correlated to measurements of the dynamic and static contact angles. The model describes two regimes, an inertial and a capillary regime, that are characterized by two distinct liquid loss processes. The semi-empirical model provides the semiconductor industry with a useful predictive tool for reducing defects associated with film pulling.
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Timothy A. Shedd, Scott D. Schuetter, Gregory F. Nellis, Chris K. Van Peski, "A model to predict the critical velocity for liquid loss from a receding meniscus", Proc. SPIE 6349, Photomask Technology 2006, 634904 (20 October 2006); doi: 10.1117/12.693286; https://doi.org/10.1117/12.693286

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